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Comput."],"published-print":{"date-parts":[[2023,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Noise poses a challenge for learning dynamical-system models because already small variations can distort the dynamics described by trajectory data. This work builds on operator inference from scientific machine learning to infer low-dimensional models from high-dimensional state trajectories polluted with noise. The presented analysis shows that, under certain conditions, the inferred operators are unbiased estimators of the well-studied projection-based reduced operators from traditional model reduction. Furthermore, the connection between operator inference and projection-based model reduction enables bounding the mean-squared errors of predictions made with the learned models with respect to traditional reduced models. The analysis also motivates an active operator inference approach that judiciously samples high-dimensional trajectories with the aim of achieving a low mean-squared error by reducing the effect of noise. Numerical experiments with high-dimensional linear and nonlinear state dynamics demonstrate that predictions obtained with active operator inference have orders of magnitude lower mean-squared errors than operator inference with traditional, equidistantly sampled trajectory data.<\/jats:p>","DOI":"10.1137\/21m1439729","type":"journal-article","created":{"date-parts":[[2023,7,5]],"date-time":"2023-07-05T10:35:23Z","timestamp":1688553323000},"page":"A1462-A1490","source":"Crossref","is-referenced-by-count":11,"title":["Active Operator Inference for Learning Low-Dimensional Dynamical-System Models from Noisy Data"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0280-3977","authenticated-orcid":true,"given":"Wayne Isaac Tan","family":"Uy","sequence":"first","affiliation":[{"name":"Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuepeng","family":"Wang","sequence":"additional","affiliation":[{"name":"Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuxiao","family":"Wen","sequence":"additional","affiliation":[{"name":"Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benjamin","family":"Peherstorfer","sequence":"additional","affiliation":[{"name":"Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,7,5]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718713"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1093\/imamci\/3.2-3.61"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/15M1041432"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2008.2006102"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2004.08.006"},{"key":"ref6","doi-asserted-by":"crossref","unstructured":"C. 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